Correct gas equation is :

Options

A. `(V_(1)T_(2))/(p_(1))=(V_(2)T_(1))/(p_(2))`
B. `(p_(1)T_(1))/(V_(1))=(p_(2)V_(2))/(T_(2))`
C. `(p_(1)V_(1))/(p_(2)V_(2))=(T_(1))/(T_(2))`
D. `(V_(1)V_(2))/(T_(1)T_(2))=p_(1)p_(2)`

Answer

C

Explanation

If temperature, volume and pressure of fixed amount (say n mole) of a gas vary from `T_(1),V_(1) and p_(1)" to " T_(2).V_(2)` and `p_(2)` respectively. Then, ideal gas equation for two states can be written as
`p_(1)V_(1)=nRT_(1)`
`"or "(p_(1)V_(1))/(T_(1))=nR" ...(i)"`
`p_(2)V_(2)=nRT_(2)`
`"or "(p_(2)V_(2))/(T_(2))=nR" ...(ii)"`
On combining Eqs. (i) and (ii), we get
`(p_(1)V_(1))/(T_(1))=(p_(2)V_(2))/(T_(2))`
`"or "(p_(1)V_(1))/(p_(2)V_(2))=(T_(1))/(T_(2))`
So, it called combined gas equation.
Hence, (c) answer is correct.